Calculus 2nd Edition Rogawski

338 CHAPTER 6 APPLICATIONS OF THE INTEGRAL
In Exercises 51 and 52, water is pumped into a spherical tank of radius
2mfrom a source located 1mbelow a hole at the bottom (Figure 5).
The density of water is 1000 kg/m 3 .
51. Calculate the work required to fill the tank.
52. Calculate the work F (h) required to fill the tank to level h meters
in the sphere.
53. A tank of mass 20 kg containing 100 kg of water (density
1000 kg/m 3 ) is raised vertically at a constant speed of 100 m/min for
one minute, during which time it leaks water at a rate of 40 kg/min.
Calculate the total work performed in raising the container.
2
Water source
FIGURE 5
1